Question

Find the indefinite integral.

∫ x^2(1-x)^6 dx

I am so lost on this. I let u=1-x so du=-dx.

After that, I'm not sure what to do.

Answer 1

go to

http://www.wolframalpha.com/input/?i=integrate+x%2F%281-x%29

type in:

integrate x^2(1-x)^6

It is a serious mess !!!

Answer 2

The only thing I know to do is multiply (1-x)^6 out (use binary coefficients)

then you have a whole string of simple ones
which is why the answer at Wolfram starts with someting times x^9

Answer 3

(1-x)^6
= 1 - 6x + 15x^2 - 20x^3 etc
multiply by x^2
so
x^2 - 6x^3 + 15x^4-20x^5 .....etc
THEN integrate
(1/3)x^3 - (3/2)x^4 + 4x^5 -(10/3)x^6 ... etc

Answer 4

whoop, that is 3 x^5 not 4 x^5

Answer 5

Otherwise I am agreeing with Wolfram

Answer 6

Get it ?